Preliminary phi-divergence test estimators for linear restrictions in a logistic regression model

Abstract

The problem of estimation of the parameters in a logistic regression model is considered under multicollinearity situation when it is suspected that the parameter of the logistic regression model may be restricted to a subspace. We study the properties of the preliminary test based on the minimum phi-divergence estimator as well as in the phi-divergence test statistic. The minimum phi-divergence estimator is a natural extension of the maximum likelihood estimator and the phi-divergence test statistics is a family of the test statistics for testing the hypothesis that the regression coefficients may be restricted to a subspace.